Several Classes of Additively Non-Regular Semirings  

作　　者：Yong Hua LI Feng Mei HUANG Yong HE 

机构地区：[1]School of Mathematical Sciences, South China Normal University, Guangdong 510631, P. R. China [2]School of Computer, Hunan University of Science and Technology, Hunan 411201, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2010年第5期775-790,共16页数学研究与评论（英文版）

基　　金：Supported by the Natural Science Foundation of Hunan Province (Grant No04JJ4001);the Scientific Research Foundation of Hunan Education Department (Grant No05A014)

摘　　要：In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings （given by M. K. Sen, S. K. MaRy, K. P. Shum, 2005） and the semirings which are subdirect products of a distributive lattice and a ring （given by S. Ghosh, 1999） to additively non-regular semirings.In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings （given by M. K. Sen, S. K. MaRy, K. P. Shum, 2005） and the semirings which are subdirect products of a distributive lattice and a ring （given by S. Ghosh, 1999） to additively non-regular semirings.

关 键 词：Green＇s  -relations subdirect product adequate semiring skew-halfring. 

分 类 号：O152.7[理学—数学]